We introduce and study an implementation technique of the mean-field dynamic-cluster method for the analysis of lattice models. The technique is characterized by two indices (n, m), where n is the size of the clusters and m denotes their overlap. For some lattice models, we find that the cluster method converges to the exact kinetics with increasing cluster size n, in a conventional way. However, for some other models it is shown that the cluster approximation predicts a phase diagram that is qualitatively incorrect even for large n. A reason for this anomalous behavior is suggested. The effect of different, but physically equivalent, representations of the same lattice model on the quality of the approximation results is also explored.PACS number(s): 05.40. +j, 64.60.Ht, 82.20. Mj, 82.65.Jv

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